Extending the work of Larson and Todorcevic,
we show there
is a model of set theory in which normal spaces are collectionwise
Hausdorff if they are either first countable or locally compact, and
yet there are no first countable $L$-spaces or compact
$S$-spaces. The model is one of the form PFA$(S)[S]$, where $S$
is a coherent Souslin tree.